Boussinesq Wave Research Articles

A numerical study of submarine–landslide–generated tsunami and its propagation in Majene, West Sulawesi

On 14th January 2021, there was a devastating earthquake (Mw 6.2) hit Mamuju and Majene, West Sulawesi, Indonesia at 18.28 UTC. According to National Disaster Management Authority, this event causes 84 casualties and 279 houses were damaged. The Sulawesi Island is situated in a very complex tectonic region, there are several thrusts and faults along the area such as Majene Thrust, Palu-Karo Thrust, Matano Fault, and Tolo Thrust that can lead to tectonic activities. One of the largest earthquakes was a 7.9 Mw in 1997 generated from North Sulawesi Megathrust that caused a catastrophic tsunami. Moreover, there were 9 tsunami events in the Makassar Strait from the year 1800 to 1999. In this research, three different scenarios of the tsunami in Majene were applied to obtain the tsunami elevation. Makassar Strait could be potentially generated tsunami wave from submarine landslides due to its steep bathymetry that will impact the coastline at Sulawesi and Kalimantan, so it is necessary to model the tsunami propagation using submarine landslide as the tsunami generation. The volume of submarine landslide had been used in tsunami submarine landslide modelling as an input. Those are included the height, width and length of the submarine landslide volume. Furthermore, the domain bathymetry was obtained from National Bathymetry (BatNas) with spacing grid of 300 m × 300 m. The submarine landslide coordinate is also needed as a source of tsunami at 2.98°S and 118.94°E. The slide angle and slope angle are also inputted in this modelling with three experimental volumes, namely 1 km3, 0.8 km3, and 0.5 km3. This submarine landslide tsunami modelling used the Non-Hydrostatic WAVE Model (NHWAVE) method to obtain tsunami wave generation. The result from NHWAVE model will be used for initial elevation of tsunami wave propagation using the Fully Nonlinear Boussinesq wave model - Total Variation Diminishing (FUNWAVE - TVD) method. The highest initial tsunami elevation value at each observation point obtained from the NHWAVE model occurred at point 18 (the closest location to the earthquake source), which is around 0.4 –1.2 m. The FUNWAVE simulation result is the tsunami wave propagation for 180 minutes later. In the 180th minute, the tsunami wave was still propagating towards the north of Sulawesi Island to the east of Kalimantan Island.

Modeling nearshore dynamics of extreme storms in complex environments of Connecticut

Flood hazard planning requires the accurate estimation of total water elevation due to predicted tide, surge, and wave runup to design flood protection structures and improve coastal risk planning for severe storms. The beach geomorphology and nearshore hydrodynamic conditions impact the conclusive flood inundation mapping in complex environments. The conventional approaches of flood modeling are limited due to either i) simple static estimates, ii) the application of a coupled circulation and phase-averaged wave models in coarse resolution, iii) failing to calibrate and validate with in-situ data, or iv) not considering sea-level rise projections in mapping the flood extent. We used a fully nonlinear Boussinesq wave model (FUNWAVE-TVD) on the nearshore area with a high-resolution grid to determine total water elevation on the shores. The model adopted the boundary conditions from coupled circulation and wave model of the Long Island Sound (Liu et al., 2020).We applied the model to Branford, Norwalk, and New Haven, CT to represent the complex topo-bathymetric features and the structural interference in shallow water wave dynamics. We compared the model results with the FEMA base flood elevation, the North Atlantic Coast Comprehensive Study (NACCS), and (Liu et al., 2020)’s Long Island Sound FVCOM-SWAVE model. The FUNWAVE-TVD model is found to model wave processes more accurately in shallow water regions compared to the empirical equation application of FEMA and coupled circulation-phase averaged model application of NACCS and FVCOM-SWAVE. We also examined local sea-level rise predictions of storms with 1% and 10% annual exceedance probability by the year 2050 in Connecticut and found that the flood extent of these two storms showed little to no difference. We suggest the planning approaches should consider the increase in the frequency of the storms in the predicted inundation zones due to sea-level rise.

Predicting Crenulate Bay Profiles from Wave Fronts: Numerical Experiments and Empirical Formulae

For crenulate-shaped bays, the coastal outline assumes a specific shape related to the predominant waves in the area: it generally consists of a tangential zone downcoast and a curved portion upcoast. Many coastal engineers have attempted to derive an expression of the headland bay shapes that emerge when a full equilibrium is reached (stable or dynamic). However, even though models for static equilibrium bays exist, they are merely of an empirical kind, lacking further insight on relationships between incident wave characteristics and beach shape. In addition, it is commonly believed that shoreline profiles tend to follow wave fronts, but this has been never fully verified. In this paper, we investigate a possible correlation between static equilibrium profiles and wave front shapes. Numerical experiments have been performed using the MIKE 21 Boussinesq Wave module, and the generated wave fronts have been compared to the hyperbolic-tangent equilibrium profile. A thoughtful analysis of results revealed that a single-headland equilibrium profile is merely the wave front translated perpendicularly to the wave direction at the headland tip, without any influence of wave period or in wave direction. A new function called the “wave-front-bay-shape equation” has been obtained, and the application and validation of this formula to the case-study bay of the Bagnoli coast (south-west of Italy) is described in the paper.

Propagation and overturning of three-dimensional Boussinesq wave packets with rotation

Simulations of fully localized internal gravity wave packets with their induced mean flow superimposed reveal that waves overturn even for initial amplitudes significantly lower than the critical amplitudes predicted by linear theory, in contrast with previous results of one- and two-dimensional wave packets without rotation.

Analytical and numerical investigation of trapped ocean waves along a submerged ridge

Abstract

Wave estimation within a port using a fully nonlinear Boussinesq wave model and artificial neural networks

An artificial neural network is developed to estimate the wave conditions within a port efficiently. Wave motions within the harbor subject to incident waves with varying combinations of offshore parameters (i.e., significant wave height, peak period, and peak direction) are simulated using the Boussinesq-type wave model to obtain a pre-calculated dataset. The outputs of the network are significant wave height and low-frequency wave height within the port. The neural network is trained on the dataset to ensure that efficient estimations for unknown cases with incident parameters similar to those in the pre-calculated cases can be provided. This is done to avoid the high computational cost of the wave model during real-time prediction. A k-fold cross-validation method is utilized to determine the optimum network among a variety of architectures. As a first verification step, the statistical results show that the network performs well when estimating unknown cases that are not included in the training process. Subsequently, the network is successfully validated against the observed in-situ data, proving the reliability of both the wave model and neural networks. Once the forecasting of offshore wave parameters is provided, the wave conditions within the port can be estimated quickly to realize the real-time prediction.

Wave Model for the Design of Sustainable Coastal Infrastructures at an Industrial Site in Tuban, East Java

This study focuses on the use of computational model in the design of a breakwater structure, which aims to determine the propagation pattern of the long-term ocean waves, in order to understand their propagation from the deep waters, and to determine the distribution of their energy around a proposed breakwater construction site. The method used is computational simulation of the wave model using the 2D Boussinesq Wave (BW) Module of MIKE21 software. The simulation used an incoming wave of 4.6 m high, which corresponds to the 100 years return-period value. The results show that the existing breakwater layout can protect the harbour by reducing the incoming waveheight by up to 75%. At the proposed design condition, the propagation pattern of the incoming wave slightly differs from the existing condition. The presence of the slopes on both sides of the channel changes the wave direction outwards due to shoaling effects, and consequently, larger concentration of wave energy occurs at some parts of the proposed breakwater design. Results from the model are useful for the design of the new breakwater structures, which is designed according to the predicted wave energy distribution.

Design of a Spun Pile Vertical Wall Breakwater for the Improvement of Damaged Cellular-Cofferdam

A new breakwater is on demand to replace the function of an existing steel sheet pile cellular-cofferdam at TPPI Tuban Port of East Java. The existing breakwater has been partially damaged due to severe corrosion and hard attack by monsoon waves. An open frame structure of spun pile vertical-wall breakwater is proposed as an alternative design. The spun pile is a pre-stressed concrete hollow cylinder pile with outer diameter 1800mm and thickness of 200mm. The spun pile lengths vary between minimum 28m to maximum 33m according to the position of hard soil against seabed. The new breakwater is designed to stand against 100yrs RP wave with Hs = 4.7m. Wave height variations around the structure are simulated using Boussinesq Wave module of MIKE21 software, while SAP2000 is used to calculate the strength of superstructure to withstand existing loads and certain load combinations. Plaxis software is used mainly to analyze substructure using existing soil data. This article describes the design process of spun pile vertical wall breakwater, started from loads calculation, then define load combinations, analyze structure in SAP2000, analyze structure in Plaxis, determination of specification and dimension, to design drawings creation.

Assessing coastal hazard from extreme storms with a phase resolving wave model: Case study of Narragansett, RI, USA

Coastal hazard at the residential scale, resulting from the combined effects of storm surge and waves including dynamic set-up and wave runup, is assessed for the local 100-year Synthetic Design Storm (SDS) in Narragansett, RI, USA, based on high resolution (2 m) simulations with the nonlinear phase-resolving Boussinesq wave model FUNWAVE. The accuracy of wave-flow-structure interaction modeling is improved using a built-up DEM, defined by adding coastal structures to the bare-earth DEM. In addition, bathymetry and topography are modified to reflect post-storm conditions based on simulating the same storm with the morphodynamic model XBeach. Comparisons of FUNWAVE results with those of the phase-averaged model STWAVE, for the same storm conditions, show that including individual wave effects increases the inundated area by 13% and maximum water levels (TWL) across the shoreline by 11%, in average; however, in high runup areas (such as along exposed structures), the predicted maximum water levels can increase by up to 100%. FUNWAVE predicts maximum runups on the order of ∼1.5Hs (with Hs the offshore significant wave height), which is consistent with empirical formulae for steep seawalls (Van der Meer, 2002), and these occur at the most exposed structures, which historical records show have been periodically damaged by large storms. The maximum momentum forces predicted by FUNWAVE are much larger than those derived from STWAVE simulations (based on linear wave theory and assuming Rayleigh distributed waves), and also occur on the most exposed structures. The study provides a quantitative assessment of the local coastal hazard associated with the selected SDS at the scale of individual structures, and stresses the importance of accurately modeling individual wave effects, runups and associated forces in coastal hazard assessment modeling studies.

A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows

This article presents a semi-discrete, multilayer set of equations describing the three-dimensional motion of an incompressible fluid bounded below by topography and above by a moving free-surface. This system is a consistent discretisation of the incompressible Euler equations, valid without assumptions on the slopes of the interfaces. Expressed as a set of conservation laws for each layer, the formulation has a clear physical interpretation and makes a seamless link between the hydrostatic Saint-Venant equations, dispersive Boussinesq-style models and the incompressible Euler equations. The associated numerical scheme, based on an approximate vertical projection and multigrid-accelerated column relaxations, provides accurate and efficient solutions for all regimes. The same model can thus be applied to study metre-scale waves, even beyond breaking, with results closely matching those obtained using small-scale Euler/Navier–Stokes models, and coastal or global scale dispersive waves, with an accuracy and efficiency comparable to extended Boussinesq wave models. The implementation is adaptive, parallel and open source as part of the Basilisk framework and the documented source codes sufficient to reproduce all results and figures are provided.

Numerical Study of the Impact of Climate Change on Irregular Wave Run-up Over Reef-Fringed Coasts

Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing. It is believed that climate change will result in a net increase in the water depth over the reef flat, a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights. For an accurate assessment of how climate change affects the safety of reef-fringed coasts, a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model, FUNWAVE-TVD. Validated with experimental data, the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs. Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise, degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the back-reef beach respectively. Variations of run-up components (i.e., spectral characteristics of run-up and mean water level) were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.

Unusual Trapped Mountain Lee Waves with Deep Vertical Penetration and Significant Stratospheric Amplitude

Abstract Simulations of the weather over the South Island of New Zealand on 28 July 2014 reveal unusual wave activity in the stratosphere. A series of short-wavelength perturbations resembling trapped lee waves were located downstream of the topography, but these waves were in the stratosphere, and their crests were oriented north–south, in contrast to both the northeast–southwest orientation of the spine of the Southern Alps and the crests of trapped waves present in the lower troposphere. Vertical cross sections through these waves show a nodal structure consistent with that of a higher-order trapped-wave mode. Eigenmode solutions to the vertical structure equation for two-dimensional, linear, Boussinesq waves were obtained for a horizontally homogeneous sounding representative of the 28 July case. These solutions include higher-order modes having large amplitude in the stratosphere that are supported by just the zonal wind component. Two of these higher-order modes correspond to trapped waves that develop in an idealized numerical simulation of the 28 July 2014 case. These higher-order modes are trapped by very strong westerly winds in the midstratosphere and are triggered by north–south-oriented features in the subrange-scale topography. In contrast, the stratospheric cross-mountain wind component is too weak to trap similar high-order modes with crest-parallel orientation.

Applications of mixed lump-solitons solutions and multi-peaks solitons for newly extended (2+1)-dimensional Boussinesq wave equation

In this work, based on the Hirota bilinear method, mixed lump-solitons solutions and multi-peaks solitons are derived for a new extended (2[Formula: see text]+[Formula: see text]1)-dimensional Boussinesq equation by using ansatz function technique with symbolic computation. Through the mixed lump-solitons, we obtained two types of interaction phenomena, first from lump-single soliton solution and other from lump-two soliton solutions and their dynamics is given by three-dimensional plots and two-dimensional contour plots by taking appropriate values of given parameters. Furthermore, we obtained new patterns of multi-peaks solitons.

Modeling Study on the Hydrodynamic Environmental Impact Caused by the Sea for Regional Construction near the Yanwo Island in Zhoushan, China

Waves are one of the most important factors affecting offshore marine engineering. Accurate calculation of wave distribution is an important prerequisite to ensure the safety of coastal engineering construction. Due to the influence of complex topography, hydrological conditions, and marine structures on the propagation of waves offshore, slowly varying topography, refraction, diffraction, reflection, shallowness, and other phenomena may occur. This article combines the MIKE21 Spetral Waves (SW) wave model and the MIKE21 Boussinesq Waves (BW) wave model which are developed by Danish Hydraulic Institute (DHI) for a joint application (SW–BW nested model). It simulates the hydrodynamic environment of the Yanwo Island scenic area, located in Zhoushan, in both large and small ranges. In addition, wave height distribution and berthing stability of different breakwater planning schemes are calculated to optimize the layout of the breakwater. Through the analysis of simulation results, it is concluded that the hydraulic performance of Scheme 2 (the broken line section on the west side is 100 m long, and that on the east is 1200 m long, and the breakwater is rotated 8 degrees counterclockwise along the axis on the basis of Scheme 1) is better than that of Scheme 1 (the broken line section on the west side is 100 m long, and that on the east is 1100 m long), which can provide a more reliable construction reference for the construction of the Yanwo Island scenic area.

Assessment of Efficiency of Array of Wave Energy Converters using Mike21-Bw Model, Near Bhagvati Bandar

The world we live in is becoming more and more dependent on electrical energy and shortage of energy is bound to happen in the nearest future. India is the third largest in terms of power generation. Global warming and climate changes are the biggest challenge faced by mankind. Use of energy resources which are renewable and green that is producing low carbon emission is the need of the day. India has invested heavily on wind energy and solar energy. Ocean wave energy generation is renewable process with minimal carbon emission as well as less land requirement. India has a long coastline and has a tremendous scope for generation of wave energy along its coastline. Wave Energy Converter (WEC) is the device used in the wave energy extraction. For making the wave energy conversion feasible, the efficiency of a WEC is required to be assessed. For the design of WEC and assessment of its efficiency numerical models are very much useful giving the flexibility of assessing a number of alternatives at a relatively low cost. An attempt is made in this paper to estimate efficiency of an array of WECs using the Boussinesq Wave Model, namely the mathematical model MIKE21-BW. A site at Bhagvati Bandar, which is identified as hotspot for wave energy generation is considered for the installation of WECs. Numerical model experiments were carried out to find optimal configuration of an array of WECs and the findings are presented in this paper.

Wave prediction in a port using a fully nonlinear Boussinesq wave model

A wave forecasting system using FUNWAVE-TVD which is based on the fully nonlinear Boussinesq equations by Chen (2006) was developed to provide an accurate wave prediction in the Port of Busan, South Korea. This system is linked to the Korea Operational Oceanographic System (KOOS) developed by Park et al. (2015). The computational domain covers a region of 9.6 km×7.0 km with a grid size of 2 m in both directions, which is sufficient to resolve short waves and dominant sea states. The total number of grid points exceeds 16 millions, making the model computational expensive. To provide real-time forecasting, an interpolation method, which is based on pre-calculated results of FUNWAVE-TVD and SWAN forecasting results at the FUNWAVE-TVD offshore boundary, was used. A total of 45 cases were pre-calculated, which took 71 days on 924 computational cores of a Linux cluster system. Wind wave generation and propagation from the deep water were computed using the SWAN in KOOS. SWAN results provided a boundary condition for the FUNWAVE-TVD forecasting system. To verify the model, wave observations were conducted at three locations inside the port in a time period of more than 7 months. A model/model comparison between FUNWAVE-TVD and SWAN was also carried out. It is found that, FUNWAVE-TVD improves the forecasting results significantly compared to SWAN which underestimates wave heights in sheltered areas due to incorrect physical mechanism of wave diffraction, as well as large wave heights caused by wave reflections inside the port.

A reliable technique for fractional modified Boussinesq and approximate long wave equations

In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology.

Tsunami Intrusion and River Ice Movement

A two-dimensional wave model coupled with ice dynamics is developed to evaluate ice effects on shallow water wave propagation on a beach and in a channel. The nonlinear Boussinesq equations with ice effects are derived and solved by the hybrid technique of the Godunov-type finite volume method and finite difference method with the third-order Runge–Kutta method for time integration. The shock capturing method enables the model to simulate complex flows over irregular topography. The model is capable of simulating wave propagations accurately, including non-hydrostatic water pressure and wave dispersions. The ice dynamic module utilizes a Lagrangian discrete parcel method, based on smoothed particle hydrodynamics. The Boussinesq wave model is validated with an analytical solution of water surface oscillation in a parabolic container, an analytical solitary wave propagation in a flat channel, and experimental data on tsunami wave propagations. The validated model is then applied to investigate the interaction between ice and tsunami wave propagation, in terms of ice attenuation on tsunami wave propagations over a beach, ice deposition on the beach driven by the tsunami wave, and ice jam formation and release in a coastal channel with the intrusion of the tsunami wave. The simulated results demonstrated the interactions between tsunami waves and surface ice, including the maximum run up, ice movement along the beach, and ice jamming in a channel.

Study of irregular wave run-up over fringing reefs based on a shock-capturing Boussinesq model

This paper presents the results of a parametric study of irregular wave run-up over fringing reefs using the shock-capturing Boussinesq wave model Funwave-TVD to better understand the role of fringing reefs in the mitigation of wave-driven flooding. Laboratory experiments were newly performed with a typical fringing reef profile and typical hydrodynamic conditions to validate the model. Experimental data shows irregular wave run-ups are dominated by the low-frequency motions and confirms the run-up resonant phenomenon over the back-reef slope, which has been revealed in previous numerical studies. It is demonstrated that irregular wave evolution and run-up over fringing reefs are reasonably reproduced by the present model with a proper grid size. However, the infragravity run-up height and highest 2% run-up height over the back-reef slope are under-predicted due to the underestimation of the infragravity wave height over the reef flat. The validated model was then utilized to model irregular wave transformations and run-ups under different conditions. Through a series of numerical experiments, the effects of key hydrodynamic and reef geometry parameters, including the reef flat width, water depth over the reef flat, fore-reef slope angle and back-reef slope angle, on the irregular wave run-up were investigated. Variations of spectral components of irregular wave run-ups were examined to better understand the physical process underlying the effect of each parameter.

The influence of climate change on tsunami-like solitary wave inundation over fringing reefs

ABSTRACTThe protective capability of fringing reefs against tsunami hazards has been reported in numerous post-disaster surveys. It is believed that global warming is changing the water level over the reef flat and reef surface roughness by sea-level rise and coral bleaching. For a better understanding of the influence of climate change on tsunami hazards over fringing reefs, this study utilized a shock-capturing Boussinesq wave model, FUNWAVE-TVD, to simulate the tsunami-like solitary wave propagation and run-up over fringing reefs. Calibrated and validated by the newly obtained experimental data, the present model with shock-capturing scheme, in which only the ratio of wave height to water depth is used to trigger wave breaking, shows reasonable prediction of solitary wave transformation and run-up height over sharply varying reef bathymetry. Numerical experiments were then carried out to investigate the effects of sea-level rise and degrading of the reef surface roughness on the solitary wave inundation distance and fluid force distribution in the inundation zone. Numerical results clearly demonstrate how tsunami hazards change within the inundation zone in response to higher water levels and lower reef roughness and suggest climate change, especially sea-level rise, will significantly increase tsunami hazards in the low-lying areas of the reef-lined coasts. Presented results are discussed for the effects of sea-level rise and coral bleaching on the solitary wave process and implications to further improve the resilience under the threat of climate change.